Graph theoretic terminology may be found in [1]}. A graph \(G\)  of order \(n\) is an ordered pair \((V, E)\)  consisting of a set \(E=E(G)\)  of edges and a set \(V=V(G)\)  of vertices such that \(|V|=n\) . We adopt standard notation and let \(m=|E(G)|\)  denote the number of edges in a graph \(G\) . A graph is simple if it contains no loops or multiple edges and it is connected if it contains no isolated vertices. If \(G\)  is a graph of order \(n\) , then its adjacency matrix is the \(n\times n\)  real symmetric matrix \(A(G)\)  whose entries are defined by setting \([A(G)]_{ij}=1\)  if vertices \(i\)  and \(j\)  are connected by an edge and \([A(G)]_{ij}= 0\)  otherwise. The spectrum of \(G\)  is the spectrum of its adjacency matrix \(A(G)\) , and is therefore real since \(A(G)\)  is Hermitian. We adopt a standard convention and write the spectrum of \(G\)  in non-increasing order,
\(\lambda _1\ge \lambda _2\ge \cdots \ge \lambda _n.\) 
